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Math 5343: "Numerical Solutions to Partial Differential Equations"

  • Meeting Times: Tu-Th 1:30pm-2:50pm

  • Office Hours: Wednesdays 1:30pm-4:30pm

  • Place : CRBL C303

  • TextBook: Computational Partial Differential Equations Using MATLAB by Jichun Li and Yi-Tung Chen.

  • Course Description: This course serves as an introduction to two very popular numerical methods to solve partial differential equations (pdes) namely finite difference methods and finite element methods. We will cover both these techniques. The class will be a healthy balance of theory and programming and students will be exposed to the latest state-of-art methods and open source software available to solve the pdes.

    Click here for the syllabus of the course.

  • Goals: The goal is twofold namely:
    1. To provide a sound mathematical background in numerical methods for pdes. This includes a description of the pdes which govern physical phemonena, the numerical methods of finite difference and finite element and the issues of convergence, stability and error analysis for the methods.

    2. To supplement the understanding of these methods, we will have a hands on experience with programming these methods through the Matlab codes provided with the textbook.
      Novices to Matlab are strongly encouraged to attend the Matlab course I will be teaching in Spring 2015. You can access the course webiste here.

  • Prerequisites: A strongly motivated student with a Calculus (I,II and III) and Linear Algebra background should be able to follow the class. Programming is not a prerequisite but a desire to learn programming is!

  • Assignments: Expect to be assessed on homeworks, class performance and attendance.

    • Announcements

    Week
    Topic for the week
    Assignments for the week
    19th-23rd January
    Introduction to Partial Differential Equations.
    None
    26th-30th January
    Introduction to Finite Difference scheme for 1D and 2D.
    None
    2nd-6th February
    Finite Difference scheme for time dependent problems, CFL condition.
    		Homework 1 posted due on 2/17
    9th-13th February
    Error Analysis, programming a Finite Difference scheme
    None
    16th-20th February
    Prelude to Finite Element method and weak formulation
    		Homework 2 posted due on 2/24
    23rd-27th February
    Continuation of Weak formulation ; stiffness, mass matrices examined.
    		Homework 3 posted due on 3/05
    2nd-6th March
  • Programming a Finite Element method
  • Discussing essential and natural boundary conditions
  • Error Analysis in 1D
    		•  Spring break Homework 4 to be posted due on 3/17
    9th-13th March
    SPRING BREAK !
    Happy Coding :-)
    16th-20th March
    Euler Equations of variational problems
    Homework 5 posted due on 3/26
    23rd-27th March
    Triangular Finite Element Spaces and interpolation
    Homework 6 posted due on 4/02
    30th March-3rd April
    Unisolvence of elements ; Well posedness of solution
    Homework 7 posted due on 4/09
    6th-10th April
    Error Analysis and programming a Finite Element methods in 2D
    Homework 8 posted due on 4/16
    13th-17th April
    Error Analysis (continued) and addressing programming issues
    Homework 9 posted due on 4/23
    20th - 24th April
    Other finite element spaces and a posteriori error analysis
    Prepare for the BIG final homework !
    27th April- 1st May
    Other finite element spaces and a posteriori error analysis
    Final Homework 10 posted due on 7th May
    4th-8th May
    A note on finite element software available; Current State of the art research in this field
    End of the classes :-)